A harmonic signal may have a fundamental frequency and one or more overtones. Harmonic signals include, for example, speech and music. A harmonic signal may have a fundamental frequency, which may be referred to as the first harmonic. A harmonic signal may include other harmonics that may occur at multiples of the first harmonic. For example, if the fundamental frequency is f at a certain time, then the other harmonics may have frequencies of 2f, 3f, and so forth.
The fundamental frequency of a harmonic signal may change over time. For example, when a person is speaking, the fundamental frequency of the speech may increase at the end of a question. A change in the frequency of a signal may be referred to as a chirp rate. The chirp rate of a harmonic signal may be different for different harmonics. For example, if the first harmonic has a chirp rate of c, then other the harmonics may have chirp rates of 2c, 3c, and so forth.
In applications, such as speech recognition, signal reconstruction, and speaker recognition, it may be desirable to determine properties of a harmonic signal over time. For example, it may be desirable to determine a pitch of the signal, a rate of change of the pitch over time, or the frequency, chirp rate, or amplitude of different harmonics.